Question

Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science,6 in English and Mathematics, 7 in Mathematics and Science; 4 in English andScience; 4 in all the three. Find how many passed(i)in English and Mathematics but not in Science(ii)in Mathematics and Science but not in English(iii)in Mathematics only(iv)in more than one subject only

Answer 1

i)21passed in English and 18 passed in mathematics not in science ii) 12 passed in mathematics 8 passed in science not in English iii)12 passed only in mathematics iv) in English 29 are passed so it is more than other subjects

Answer 2

Answer and explanation:

Given :

Total number of students = 100

Number of students passed in English = 15

Number of students passed in Mathematics = 12

Number of students passed in Science = 8

Number of students passed in English and Mathematics = 6

Number of students passed in Mathematics and Science = 7

Number of students passed in English and Science = 4

Number of students passed in all three = 4

To find : How many passed in following options ?

Solution :

Let U be the total number of students, E, M and S be the number of students passed in English, Mathematics and Science respectively

n(M ∩ S ∩ E) = a = 4

n(M ∩ S) = a + d = 7

⇒ 4 + d = 7

⇒ d = 3

n(M ∩ E) = a + b = 6

⇒ 4 + b = 6

⇒ b = 2

n(S ∩ E) = a + c = 4

⇒ 4 + c = 4

⇒ c = 0

n(M) = e + d + a + b = 12

⇒ e + 4 + 3 + 2 = 12

⇒ e + 9 = 12

⇒ e = 3

n(E) = g + c + a + b = 15

⇒ g + 0 + 4 + 2 = 15

⇒ g + 6 = 15

⇒ g = 9

n(S) = f + c + a + d = 8

⇒ f + 0 + 4 + 3 = 8

⇒ f + 7 = 8

⇒ f = 1

(i) Number of students passed in English and Mathematics but not in Science is

b = 2

(ii) Number of students in Mathematics and Science but not in English is

d = 3

(iii) Number of students in Mathematics only is

e = 3

(iv) Number of students in more than one subject only is

P= a + b + c + d

P= 4 + 3 + 2 + 0

P= 9